4 children each have some beads, the mean number of beads is 8 Rajiv brings some more beads. The mean number of 5 children is now 9 what is the numberx of beads Rajiv brings

Answers

Answer 1

Answer:

The number of beads Rajiv brings is: 13

Step-by-step explanation:

Make a plan:

In this question, we need to use the formula of means to solve the. We can set the number of beads Rajiv brings as X, and use the formula of mean to get the total number of beads that the Four(4) children have and the total number of beads that the Five(5) children have.

Solve the problem:

Four(4) children each have some beads, the mean number of beads is: 8

We can get the total number of beads the Four(4) children have:

        4 * 8 = 32

Rajiv brings some more beads:

We set the number of beads Rajiv brings as:

x, so the total number of beads that the Five(5) children have is:

32  +  x

The mean number of the Five(5) children is now: 9

We can get the total number of beads that the Five(5) children have:

      5  *  9   =  45

Now, we have the equation:

     32 +  x    =    45

      x  +  32  =    45

           -  32  =   -32

       x            =     13

By solving the above equation, you can get:

x  =  13

Hence, The number of beads Rajiv brings is:

       13

Hope this helps!


Related Questions

Numbers and operations
show work on paper if possible :)

Answers

Answer:

B. $5.99

Step-by-step explanation:

Let's start by finding the total cost of the sodas. We know that there were 5 sodas and each cost $0.75, so the total cost of the sodas is:

5 * $0.75 = $3.75

Next, we need to subtract the cost of the sodas from the total cost before tax to find the cost of the pizzas:

$33.70 - $3.75 = $29.95

Finally, we can divide the cost of the pizzas by the number of pizzas to find the cost of each pizza:

$29.95 ÷ 5 = $5.99

Therefore, the cost of each pizza pie was $5.99. Answer choice B is correct.

Linear Programming Project
You are the new owner of a music shop in Greenwood. The previous owner
fled the city to join the circus as a magician. Your first duty as new owner
and store manager is to create an advertising plan based on the budget
available. You must figure out how many magazines and TV ads to
purchase.
TV ads cost $600 per airing.
Magazine ads cost $1200 per issue.
Your total advertising budget is $9,000.
1. If we let x = TV ads and y = magazine ads, write an inequality for our
advertising budget.
500 x + 1200y <= 9000
2. Due to space limitations, the magazine publishers tell us that we are only
allowed to purchase up to 6 magazine ads. Write an inequality for this
constraint. y<= 6
3. The television station called to say that we are only allowed to purchase
up to 7 TV ads. Write an inequality for this constraint.
X<=7
4. It is impossible to buy a negative number of TV ads. Write an inequality
for this constraint.
-1 -5. It is impossible to buy a negative number of magazine ads. Write an
inequality for this constraint.
-1 Use the points (1, 150) and (6, 900) to estimate the line of best fit.
1. Find the slope of the line.
2. Write the equation of the line
3. What does the slope tell you about how each TV ad affects sale
For every TV ad, CD sales increased by about
Use the points (1, 100) and (8, 800) to estimate the line of best fit.
1. Find the slope of the line.
2. Write the equation of the line.
3. What does the slope tell you about how each magazine ad affer
sales?
CD sales increased by about...?

Answers

1)

When the points (1, 150) and (6, 900) are used:

a)

Slope of line is 150.

Given points,

(1, 150) and (6, 900)

Slope of a line passing from two points:

Slope = y2 - y1 / x2 - x1

Slope = 900 - 150 / 6 - 1

Slope = 150

b)

Equation of line :

Y = mx + c

m = slope of line

c = y intercept

Here,

Slope =150

Hence the equation of line is:

y = 150x

c)

For every TV ad, CD sales increased by about 150 as the slope of line is + 150 which indicates the increase in  sales of CD .

2)

When the points (1, 100) and (8, 800) ae used:

a)

Slope of line is 100.

Given points,

(1, 100) and (8, 800)

Slope of a line passing from two points:

Slope = y2 - y1 / x2 - x1

Slope = 800 - 100 / 8 - 1

Slope = 100

b)

Equation of line :

Y = mx + c

m = slope of line

c = y intercept

Here,

Slope =100

Hence the equation of line is:

y = 100x

c)

For  every magazine ad, CD sales increased by about 100, as the slope of line is + 100 which indicates the increase in  sales of CD .

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Number of dogs: 47, 38, 72, 56, 40, 64, 30, 80, 66, 51. Use the same data set from the previous question.
What is the range for the data set?

What is the interquartile range (IQR) for the data set?

Answers

Answer:

To find the range of a data set, we subtract the minimum value from the maximum value.

Given the data set: 47, 38, 72, 56, 40, 64, 30, 80, 66, 51

The minimum value is 30, and the maximum value is 80.

Range = Maximum value - Minimum value

= 80 - 30

= 50

Therefore, the range for the data set is 50.

To find the interquartile range (IQR), we need to determine the values of the first quartile (Q1) and the third quartile (Q3) and then calculate the difference between them.

First, we need to order the data set in ascending order:

30, 38, 40, 47, 51, 56, 64, 66, 72, 80

Q1 represents the 25th percentile. Q3 represents the 75th percentile.

To find Q1, we take the average of the values at the 25th and 26th positions (since it falls between 38 and 40):

Q1 = (38 + 40) / 2

= 78 / 2

= 39

To find Q3, we take the average of the values at the 75th and 76th positions (since it falls between 66 and 72):

Q3 = (66 + 72) / 2

= 138 / 2

= 69

Now, we can calculate the interquartile range (IQR):

IQR = Q3 - Q1

= 69 - 39

= 30

Therefore, the interquartile range (IQR) for the given data set is 30.

How many quarts of whipping cream that is 36% butterfat must be mixed with 4 quarts of half and half that is 12% butterfat to make light cream that is 18% butterfat.

Answers

Approximately 1.33 quarts of whipping cream should be mixed with 4 quarts of half and half to obtain a light cream with a 18% butterfat content.

Let's denote the number of quarts of whipping cream that needs to be mixed as "x". We know that the whipping cream has a butterfat percentage of 36% and the half and half has a butterfat percentage of 12%. We want to determine the quantity of whipping cream needed to create a mixture with a butterfat percentage of 18%.

To solve this problem, we can use the concept of weighted averages. The amount of butterfat contributed by the whipping cream is 0.36x, and the amount contributed by the half and half is 0.12 * 4 = 0.48.

The total amount of butterfat in the resulting mixture is 0.18 * (x + 4) since we are aiming for an 18% butterfat content in the final mixture.

Setting up an equation based on the butterfat content, we have:

0.36x + 0.48 = 0.18(x + 4)

Simplifying the equation:

0.36x + 0.48 = 0.18x + 0.72

0.36x - 0.18x = 0.72 - 0.48

0.18x = 0.24

x = 0.24 / 0.18

x = 1.33...

Therefore, approximately 1.33 quarts of whipping cream should be mixed with 4 quarts of half and half to obtain a light cream with a 18% butterfat content.

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Which is the graph of f(x) = (x-1)(x + 4)?
O
2
AV
2
--2-
O
6
O

Answers

Answer:

The bottom one

Step-by-step explanation:

Notice that the graph is an upward opening parabola and passes through the x-axis at the x-intercepts x=1 and x=-4. These are our zeroes that allow f(x)=0 by the Zero Product Property.

A water sample shows 0.016 grams of some trace element for every cubic centimeter of water. Adam uses a container in the shape of a right cylinder with a diameter of 11 cm and a height of 12 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Adam collected? Round your answer to the nearest tenth.

Answers

Answer:

18.2 grams

Step-by-step explanation:

Since the base diameter of the cylindrical container is d=11 cm, so its radius r is:

[tex]r=\frac{d}{2}=\frac{11}{2}=5.5[/tex]

Then, the volume V of the cylindrical container with radius r=5.5 cm and height h=12 cm is:

[tex]V=\pi r^{2}h=\pi \times 5.5^{2}\times 12=363\pi[/tex]

Since the water sample contains 0.016g of trace element for every cubic centimeter of water, so amount of trace element collected by the container of volume [tex]V=363\pi[/tex] cubic centimeters is:

[tex]0.016 g/cm^{3}\times 363\pi~cm^{3}=18.2g[/tex]

find the volume of the following solid figures​

Answers

The volume of the solid figures are:

1. 480 cm³

2. 1000 m³

3. 141.43 cm³

4. 60.48 cm³

5. 16971.43 mm³

How to find the volume of solid figures​?

1. The volume of a cuboid is given by the formula:

V = l * w * h

where l is the length, w is the width and h is the height

We have:

l = 12 cm

w = 5 cm

h = 8 cm

V = 12 * 5 * 8

V = 480 cm³

2. The volume of a cube is given by the formula:

V = l³

where l is the side length

We have:

l = 10m

V = 10³

V = 1000 m³

3. The volume of a cylinder is given by the formula:

V = πr²h

where r is the radius and h is the height

We have:

r = 3 cm

h = 5 cm

V = 22/7 * 3² * 5

V = 141.43 cm³

4. This is also a cuboid.

We have:

l = 4.5 cm

w = 3.2 cm

h = 4.2 cm

V = 4.5 * 3.2 * 4.2

V = 60.48 cm³

5. This is also a cylinder.

We have:

r = 30/2 = 15 mm

h = 24 mm

V = 22/7 * 15² * 24

V = 16971.43 mm³

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Mina has 462 flowers if she wants to put nine flowers in each phase how many for vases will she have how many flowers will she have left over

Answers

She will use 51 vases and have 3 flowers left

Please help with these two questions)l!!

Answers

The integral of xe^(7x) dx is equal to (1/7) xe^(7x) - (1/49) e^(7x) + C, where C is the constant of integration.

The integral of x cos(8x) dx is equal to (1/8) x sin(8x) + (1/64) * cos(8x) + C, where C is the constant of integration.

We have,

To solve the given integrals using integration by parts, we follow the formula:

∫u dv = uv - ∫v du

Let's solve each integral step by step:

∫xe^(7x) dx ; u = x, dv = e^(7x) dx

Taking the derivatives and integrals:

du = dx

v = ∫e^(7x) dx = (1/7) * e^(7x)

Applying the integration by parts formula:

∫xe^(7x) dx = uv - ∫v du

= x * (1/7) * e^(7x) - ∫(1/7) * e^(7x) dx

= (1/7) * xe^(7x) - (1/49) * e^(7x) + C

And,

∫x cos(8x) dx ; u = x, dv = cos(8x) dx

Taking the derivatives and integrals:

du = dx

v = ∫cos(8x) dx = (1/8) * sin(8x)

Applying the integration by parts formula:

∫x cos(8x) dx = uv - ∫v du

= x * (1/8) * sin(8x) - ∫(1/8) * sin(8x) dx

= (1/8) * x * sin(8x) + (1/64) * cos(8x) + C

Therefore,

The integral of xe^(7x) dx is equal to (1/7) xe^(7x) - (1/49) e^(7x) + C, where C is the constant of integration.

The integral of x cos(8x) dx is equal to (1/8) x sin(8x) + (1/64) * cos(8x) + C, where C is the constant of integration.

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Last year and investor purchased 115 shares of stock A at $90 per share

Answers

The difference in overall loss or gain between sell at the current day's high price or low price is found tp be the difference in overall gain as $280.10

The third option is correct.

How do we calculate?

For stock A:

High price value: 115 shares * $105.19 per share = $12,084.85

Low price value: 115 shares * $103.25 per share = $11,858.75

For stock B:

High price value: 30 shares * $145.18 per share = $4,355.40

Low price value: 30 shares * $143.28 per share = $4,298.40

The overall value at high price:

$12,084.85 + $4,355.40

= $16,440.25

The overall value at low price:

$11,858.75 + $4,298.40

= $16,157.15

In conclusion, the difference in overall gain or loss:

$16,440.25 - $16,157.15 = $280.10

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someone please help me solve this ​

Answers

Answer:

161.67 square feet

Step-by-step explanation:

The explanation is attached below.

Area of rectangle = length * width

=> Area of ABIJ = (7 * 6)ft^2 = 42 ft^2

=> Area of IJHG = (5 * 7)ft^2 = 35 ft^2
=> Area of HGCD = (7.81 * 7)ft^2 = 54.67 ft^2

=> Area of triangle = (EIH) = JFG = 1/2 * Base * height

EIH = 1/2 * 6 * 5 = 15 ft^2

JFG = 1/2 * 6 * 5 = 15 ft^2

Total area = (42 + 35 + 54.67 + 15 + 15)ft^2 = 161.67 ft^2


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5x = 50. Find x. PLS HELP PLS

Answers

Answer:

[tex]\Huge \boxed{\boxed{x = 10}}[/tex]

Step-by-step explanation:

To solve the equation [tex]5x = 50[/tex] and find the value of [tex]x[/tex], we need to isolate [tex]x[/tex] on one side of the equation.

Step 1: Divide both sides of the equation by 5.

[tex]\frac{5x}{5} = \frac{50}{5}[/tex]

Step 2: Simplify this expression

[tex]x = 10[/tex]

Therefore, the solution to the equation [tex]\boldsf{5x = 50}[/tex] is [tex]x = 10[/tex].

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Housing prices in a small town are normally distributed with a mean of
131,000 and a standard deviation of 8,000
. Use the empirical rule to complete the following statement.

Answers

About 95% of the housing Prices are between (µ - 2σ) and (µ + 2σ).About 99.7% of the housing prices are between (µ - 3σ) and (µ + 3σ)

Given that housing prices in a small town are normally distributed with a mean of µ. We are to use the empirical rule to complete the following statement.

The empirical rule states that in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean,

and approximately 99.7% of the data falls within three standard deviations of the mean.Since we do not have information about the standard deviation of the housing prices,

we cannot provide exact values for the empirical rule. However, we can make some general statements:

About 68% of the housing prices are between (µ - σ) and (µ + σ).

About 95% of the housing prices are between (µ - 2σ) and (µ + 2σ).About 99.7% of the housing prices are between (µ - 3σ) and (µ + 3σ)

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A
-2+
Which graph represents the
function y = tan x?
B
2T
2T
D
-2+1
21
4+

2T
2πT

Answers

The graph that represents the function y= tanx is Option A.

What is the description of the above function?

The graph of y =tan (x) is a periodic function that has vertical asymptotes at x = (n + 1/2)π, where n is an integer.

It oscillates between positive and   negative infinity, creating a wave-  like pattern.

It has a repeating pattern of sharp peaks and valleys, exhibiting both positive and negative slopes.

Thus, option A is the correct answer.

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What does 5^6 x 4=
.
Zzzzzzzzzz

Answers

62,500. Have a good day!!
62,000. I think. I could be wrong

A data set is normally distributed with a mean of 27 and a standard deviation of 3.5. About what percent of the data is greater than 34?

Answers

Answer:

Approximately 2.5% of the data is greater than 34.

Step-by-step explanation:

To solve this problem, we need to use the empirical rule (also known as the 68-95-99.7 rule) for a normal distribution. This rule states that about 68% of values lie within 1 standard deviation of the mean, about 95% of the values lie within 2 standard deviations of the mean, and about 99.7% of the values lie within 3 standard deviations of the mean.

The mean of the dataset is 27, and the standard deviation is 3.5.

34 is exactly 2 standard deviations away from the mean (since 27 + 2*3.5 = 34). According to the empirical rule, about 95% of the data falls within this range. This means that about 5% of the data is outside of this range.

Since the normal distribution is symmetrical, the data outside of 2 standard deviations is equally split between values that are too large and too small. Hence, about half of this 5%, or 2.5%, is greater than 34.

Therefore, approximately 2.5% of the data is greater than 34.

The Puyer Corporation makes and sells only one product called a Deb. The company is in the process of prepon
The following budget data are available
Advertising
Executive salaries
Depreciation on office equipment
Other
$ 51,960
$ 21,900
Variable Cost Per
Deb Sold
All of these expenses (except depreciation) are paid in cash in the month they are incurred
If the company has budgeted to sell 16,900 Debs in February, then the total budgeted fixed selling and administra

Answers

The Puyer Corporation has budgeted fixed selling and administrative expenses of $73,860 for February.

How to solve

This includes advertising of $51,960, executive salaries of $21,900, and other expenses of $9,900.

The variable cost per Deb sold is $2.50. If the company sells 16,900 Debs in February, then the total budgeted selling and administrative expenses will be $89,760.

The total budget spending is given as:

$73,860 + (16,900 * $2.50) = $89,760

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Leandra is renting a car for one week. The total cost to rent the car includes a weekly rate plus an additional charge per mile driven. Which graph shows the correct labels for the axes to describe the total cost Leandra will pay to rent the car for one week?

Answers

The correct labels for the axes to describe the total cost Leandra will pay to rent the car for one week is represented in option (B).

Explanation:  

In the given scenario, we are given that Leandra is renting a car for one week. The total cost to rent the car includes a weekly rate plus an additional charge per mile driven.

We can make the following points to obtain the correct labels for the axes to describe the total cost Leandra will pay to rent the car for one week

Let, x = Number of miles driven y = Total costLeandra is renting a car for one week.

Hence, we have the following given information:Total cost is a function of number of miles driven. Thus, the dependent variable is y, the Total cost.Weekly rate is a fixed cost and additional charge per mile driven is variable cost.

Hence, independent variable is x, the number of miles driven. Thus, x represents the number of miles driven and y represents the total cost to rent the car for one week.

The graph should show the number of miles driven on the x-axis and the corresponding total cost on the y-axis.The correct labels for the axes to describe the total cost Leandra will pay to rent the car for one week is represented in option (B) which is given as follows:

x-axis represents the number of miles driven in the car during one week, and y-axis represents the total cost Leandra will pay to rent the car for one week.

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note the full question maybe:

Which graph correctly labels the axes for the total cost (y-axis) Leandra will pay to rent a car for one week based on the number of miles driven (x-axis)?

PLS HELP ASAP!! I DONT UNDERSTAND…

3) There are a lot of spiders in Oklahoma. One colony, located in Edmond, Oklahoma has a total of 1.6 x 10^3 spiders living there. A second colony, located in Tulsa, Oklahoma has a total of 3.3 x 10^5 spiders living there. How does the size of the spider colony in Edmond compare to the one in Tulsa?

A) 2 times smaller
B) 20 times larger
C) 200 times larger
D) 20 times smaller

Answers

Answer:  C  200 times larger

Step-by-step explanation:

If you want to compare Edmond to Tulsa

Edmond = 1.6 x 10^3

Tulsa  = 3.3 x 10^5

10 to the power of anything means 1 and what ever that power is, that's how many 0's you put on.

Ex. 10^3 = 1000

10^5 = 100000

So Edmond = 1.6 x 1000

Tulsa = 3.3 x 100000

If you multply by 10's 100's etc.  the amount of 0's you have is how many you will move your decimal point

So Edmond = 1600

Tulsa = 330000

You can see that when comparing edmond to tulsa it got a lot larger.  200 times larger.

Megan has to spinners. It’s been one is divided into six equal parts. Spenard two is divided into four equal parts. If she spends both spinners what is the probability that’s been a one will land on for an spinner to land on Blue?

Answers

The probability that spinner one will land on four, and spinner two will land on blue is (1/24) x (2/24) = 1/288, or approximately 0.3%.

Megan has two spinners with one spinner divided into six equal parts, while the second spinner is divided into four equal parts. The probability that spinner one will land on four, and spinner two will land on blue is required.

The fundamental principle of probability states that the probability of an event happening is the number of favorable outcomes to the total number of outcomes.

To find the probability, it is essential to determine the total number of outcomes by multiplying the number of sections on each spinner.

The total number of outcomes = (Number of sections in spinner one) x (Number of sections in spinner two)

Number of sections in spinner one = 6Number of sections in spinner two = 4Total number of outcomes

= 6 x 4 = 24

The number of outcomes that will result in spinner one landing on four is one, and the number of outcomes that will result in spinner two landing on blue is two.

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Could u help me to pick the answer please I really need answer right now ​

Answers

Answer:

A

Step-by-step explanation:

Question 2: Solve each of the equations below (a) x² + 6x +8=0 (d) y² + 3y -4 = 0 (g) y² - 10y + 25 = 0 (1) y² +10y + 24 = 0 (m) y² - 13y +22=0 (p) x² - 11x + 18 = 0 (s) m²-m-56=0 (v) x²-38x+72 = 0 (y) g²-12g-64 = 0 (b) x² + 7x + 12 = 0 (e) x² - 2x - 8 = 0 (h) y² - 4y - 45 = 0 (k) x² + 9x + 18 = 0 (n) x² + x - 12 = 0 (q) y² - 14y +48 = 0 (t) y² + 22y + 96 = 0 (w) x² + 14x-51=0 (z) y² + 22y + 121 = 0 (c) y² + 7y + 10 = 0 (f) m²-7m+12=0 (1) x²-x-56=0 (1) x² + 23x+22=0 (0) m²-6m-27 = 0 (r) x² - 15x+56= 0 (u) k²-18k-88=0 (x) y² + 32y + 240 = 0​

Answers

Answer:

(a) x² + 6x + 8 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 1, b = 6, and c = 8

Substituting the values, we get:

x = (-6 ± sqrt(6² - 4(1)(8))) / 2(1)

x = (-6 ± sqrt(36 - 32)) / 2

x = (-6 ± sqrt(4)) / 2

x = (-6 ± 2) / 2

x = -4 or -2

Therefore, the solutions are x = -4 or x = -2.

(b) x² + 7x + 12 = 0

We can factorize this quadratic equation as:

x² + 7x + 12 = (x + 3)(x + 4)

Therefore, the solutions are x = -3 or x = -4.

(c) y² + 7y + 10 = 0

We can factorize this quadratic equation as:

y² + 7y + 10 = (y + 2)(y + 5)

Therefore, the solutions are y = -2 or y = -5.

(d) y² + 3y - 4 = 0

We can factorize this quadratic equation as:

y² + 3y - 4 = (y + 4)(y - 1)

Therefore, the solutions are y = -4 or y = 1.

(e) x² - 2x - 8 = 0

We can factorize this quadratic equation as:

x² - 2x - 8 = (x - 4)(x + 2)

Therefore, the solutions are x = 4 or x = -2.

(f) m² - 7m + 12 = 0

We can factorize this quadratic equation as:

m² - 7m + 12 = (m - 3)(m - 4)

Therefore, the solutions are m = 3 or m = 4.

(g) y² - 10y + 25 = 0

We can factorize this quadratic equation as:

y² - 10y + 25 = (y - 5)²

Therefore, the only solution is y = 5.

(h) y² - 4y - 45 = 0

We can factorize this quadratic equation as:

y² - 4y - 45 = (y - 9)(y + 5)

Therefore, the solutions are y = 9 or y = -5.

(k) x² + 9x + 18 = 0

We can factorize this quadratic equation as:

x² +9x + 18 = (x + 3)(x + 6)

Therefore, the solutions are x = -3 or x = -6.

(m) y² - 13y + 22 = 0

We can factorize this quadratic equation as:

y² - 13y + 22 = (y - 2)(y - 11)

Therefore, the solutions are y = 2 or y = 11.

(n) x² + x - 12 = 0

We can factorize this quadratic equation as:

x² + x - 12 = (x + 4)(x - 3)

Therefore, the solutions are x = -4 or x = 3.

(p) x² - 11x + 18 = 0

We can factorize this quadratic equation as:

x² - 11x + 18 = (x - 2)(x - 9)

Therefore, the solutions are x = 2 or x = 9.

(q) y² - 14y + 48 = 0

We can factorize this quadratic equation as:

y² - 14y + 48 = (y - 6)(y - 8)

Therefore, the solutions are y = 6 or y = 8.

(s) m² - m - 56 = 0

We can factorize this quadratic equation as:

m² - m - 56 = (m- 8)(m + 7)

Therefore, the solutions are m = 8 or m = -7.

(t) y² + 22y + 96 = 0

We can factorize this quadratic equation as:

y² + 22y + 96 = (y + 12)(y + 8)

Therefore, the solutions are y = -12 or y = -8.

(v) x² - 38x + 72 = 0

We can factorize this quadratic equation as:

x² - 38x + 72 = (x - 2)(x - 36)

Therefore, the solutions are x = 2 or x = 36.

(w) x² + 14x - 51 = 0

We can factorize this quadratic equation as:

x² + 14x - 51 = (x + 17)(x - 3)

Therefore, the solutions are x = -17 or x = 3.

(y) g² - 12g - 64 = 0

We can factorize this quadratic equation as:

g² - 12g - 64 = (g - 8)(g - 4)

Therefore, the solutions are g = 8 or g = 4.

(z) y² + 22y + 121 = 0

We can factorize this quadratic equation as:

y² + 22y + 121 = (y+ 11)²

Therefore, the only solution is y = -11.

(1) y² + 10y + 24 = 0

We can factorize this quadratic equation as:

y² + 10y + 24 = (y + 4)(y + 6)

Therefore, the solutions are y = -4 or y = -6.

(1) x² - x - 56 = 0

We can factorize this quadratic equation as:

x² - x - 56 = (x - 8)(x + 7)

Therefore, the solutions are x = 8 or x = -7.

(1) x² + 23x + 22 = 0

We can factorize this quadratic equation as:

x² + 23x + 22 = (x + 1)(x + 22)

Therefore, the solutions are x = -1 or x = -22.

(0) m² - 6m - 27 = 0

We can factorize this quadratic equation as:

m² - 6m - 27 = (m - 9)(m + 3)

Therefore, the solutions are m = 9 or m = -3.

(r) x² - 15x + 56 = 0

We can factorize this quadratic equation as:

x² - 15x + 56 = (x - 7)(x - 8)

Therefore, the solutions are x = 7 or x = 8.

(u) k² - 18k - 88 = 0

We can factorize this quadratic equation as:

k² - 18k - 88 = (k - 2)(k - 16)

Therefore, the solutions are k = 2 or k = 16.

(x) y² + 32y + 240 = 0

We can factorize this quadratic equation as:

y² + 32y + 240 = (y + 12)(y + 20)

Therefore, the solutions are y = -12 or y = -20.

Hope this helps!

HELP NEEDED PLEASEEE

Answers

b) -x

explanation: The Middle Term of a Binomial Expansion is the term that comes in the middle of the expansion of the binomial, given by the Binomial Theorem. If the power of expansion of the sum or difference of two terms is an even number, then there is only one middle term. Otherwise, there are two middle terms.

Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 5: zeroes:3, -i;9+i
Let a represent the leading coefficient. The polynomial is f(x)=a(

Answers

The polynomial f(x) with real coefficients and the given zeros is:

f(x) = x^3 - (12 + i)x^2 + (x - 3 - 2i)x + 27x + (27 + 3i)

To form a polynomial with degree 5 and the given zeros, we can start by writing the factors corresponding to each zero.

The zero 3 gives us the factor (x - 3).

The zero -i gives us the factor (x + i) since complex zeros always come in conjugate pairs.

The zero 9+i gives us the factor (x - (9+i)).

Now, we can multiply these factors together to obtain the polynomial:

f(x) = (x - 3)(x + i)(x - (9+i))

Next, we simplify the expression:

f(x) = (x - 3)(x + i)(x - 9 - i)

Expanding the product, we have:

f(x) = (x^2 + xi - 3x - 3i)(x - 9 - i)

Multiplying further:

f(x) = (x^3 - 9x^2 - ix^2 + xi - 3x^2 + 27x + 3ix - 3xi - 27i - 3x + 27 + 3i)

Combining like terms:

f(x) = x^3 - (9 + i)x^2 - 3x^2 + (x - 3 - 3i)x + 27x + (27 + 3i)

Simplifying:

f(x) = x^3 - (12 + i)x^2 + (x - 3 - 2i)x + 27x + (27 + 3i)

The polynomial f(x) with real coefficients and the given zeros is:

f(x) = x^3 - (12 + i)x^2 + (x - 3 - 2i)x + 27x + (27 + 3i)

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Luis scored 84 on the exam.
Find the z-score for Luis's exam grade. Round to two decimal places.

Answers

Mean: also known as the average is a measure of central tendency in a dataset. It is calculated by summing up all the values in the dataset and dividing the sum by the total number of values.

Standard deviation: The standard deviation is a measure of the dispersion of data around the mean in a dataset.t quantifies the average amount by which each data point in the dataset varies from the mean. A higher standard deviation indicates greater variability or dispersion of the data points, while a lower standard deviation suggests that the data points are closer to the mean. The standard deviation is typically represented by the symbol σ (sigma).

Z-Score: The z-score (also known as the standard score) is a statistical measurement that indicates how many standard deviations an individual data point is from the mean of a distribution. It allows you to compare and understand the relative position of a particular data point within a dataset.

The formula to calculate it is:  Z = (x - μ) / σ where:

Z = Z-score

x = data point

μ = mean

σ =  standard deviation

To calculate the z-score for Luis's exam grade, we can use the formula:

z = (x - μ) / σ

Where:

x = Luis's exam grade (84)

μ = Mean (81)

σ = Standard deviation (2.5)

Substituting the given values into the formula, we have:

z = (84 - 81) / 2.5

z = 3 / 2.5

z = 1.20

Rounding to two decimal places, the z-score for Luis's exam grade is 1.20.

if you subtract 1/8 from a number and multiply the result by 1/4 you get 1/16. what is the number

Answers

Answer:

(x - 1/8) * 1/4 = 1/16

x - 1/8 = 1/16

x = 1/16 + 1/8

x = 3/8

A man undertakes to pay off a debt of Rs. 622500 by monthly installments, he pays Rs. 10000 in the first month and continually increases the installments in every subsequent month by Rs. 100. In what time will the debt be cleared up?​

Answers

The debt will be cleared in approximately 158 months.

In how many months will the debt be cleared?

The monthly installment starts at Rs. 10,000 and increases by Rs. 100 each month. We can set up an arithmetic progression to represent the installment amounts:

10,000, 10,100, 10,200, ...

The nth term of this arithmetic progression can be calculated using the formula:

an = a1 + (n-1)d

where:

an = nth term of the sequence

a1 = first term of the sequence

d = common difference between the terms

In this case, a1 = 10,000 and d = 100.

Now we need to find the value of n such that the sum of the first n terms of the sequence exceeds or equals Rs. 622,500.

The sum of the first n terms of an arithmetic sequence can be calculated using the formula:

Sn = (n/2)(2a1 + (n-1)d)

We need to solve the equation:

Sn >= 622,500

Substituting the values, we have:

(n/2)(2*10,000 + (n-1)*100) >= 622,500

Simplifying the equation, we can solve for n:

n^2 + 199n - 614000 = 0

Using the quadratic formula, we find that:

n ≈ 157.37 or n ≈ -356.37

Since we cannot have a negative number of months, we take n ≈ 157.37. Therefore, it will take approximately 158 months (rounded up) to clear the debt.

Hence, the debt will be cleared in approximately 158 months.

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Someone please help me wit this

Answers

[tex](\sin \theta)^2+\left(\dfrac{9}{10}\right)^2=1\\\\(\sin \theta)^2+\dfrac{81}{100}=1\\\\(\sin \theta)^2=\dfrac{19}{100}\\\\\sin\theta=\sqrt{\dfrac{19}{100}}=\dfrac{\sqrt{19}}{10}[/tex]

Table of valúes y=8x-4

Answers

Here's a table of values for the equation y = 8x - 4:

The table below show the input and output values of the equation.

x y

0 -4

1 4

2 12

3 20

4 28

5 36

6 44

7 52

8 60

9 68

10 76

These values represent the corresponding values of y when you substitute different values of x into the equation y = 8x - 4.

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A polynomial f(x) has a lead coefficient of one and exactly three distinct zeros. Find the polynomial that uld go with this (multiply it all out) x = -2 is a zero with a multiplicity of one is a zero with a multiplicity of two x = 3 X = 1 is a zero with a multiplicity of one 0

Answers

If x = -2 is a zero with a multiplicity of one, x = 3 is a zero with a multiplicity of two, and x = 1 is a zero with a multiplicity of one, then the polynomial can be written in factored form as:

[tex]f(x) = (x + 2)(x - 3)^2(x - 1)[/tex]

To find the polynomial in expanded form, we can use the distributive property and the rules of exponents:

[tex]f(x) = (x + 2)(x - 3)(x - 3)(x - 1)\\= (x^2 - x - 6)(x - 3)(x - 1)\\= (x^3 - 4x^2 + 3x + 18)(x - 1)\\= x^4 - 5x^3 + 6x^2 + 4x + 18[/tex]

Therefore, the polynomial that has a lead coefficient of one and exactly three distinct zeros, with x = -2 as a zero with multiplicity of one, x = 3 as a zero with multiplicity of two, and x = 1 as a zero with multiplicity of one, is:

[tex]f(x) = x^4 - 5x^3 + 6x^2 + 4x + 18[/tex]

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